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Answered 2010-12-08 14:40:05
A linear relationship exists between two variables if, when you plot their values on a coordinate system, you get a straight line, or values that would "average out" to be a straight line. The line cannot be perfectly horizontal or vertical. There are many relationships among variables that give rise to curved plots as well.
The variables in the following example are not independent of one another, but serve as an easy way to imagine the plots described above. The variables are age (our sample will be 1,000 children currently in school ages 7 to 14) and years of school completed. If we plot individuals by age along the X axis, and then go up and plot their completed years of school along the Y axis, we will have 1,000 points on the grid that will be reasonably close to a straight line. Eliminate children who have repeated a grade, and it surely will be very close to a straight line. The variables have a linear relationship.
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